Stability and bifurcation of compressed elastic cylindrical tubes

The axial compression of cylindrical tubes is considered from the point of view of both bifurcation and stability. The paper considers mainly compressible hyperelastic materials and looks at all modes of bifurcation. Some general results are obtained and other aspects are illustrated with numerical results based on a compressible neo-Hookean material. In particular it is shown that in certain circumstances higher order modes can be the dominant mode. It is also shown that there are two distinct forms of the barrelling mode for shorter cylinders. This is shown by calculating the eigenfunction associated with the two distinct bifurcation points.